Expanding the given expression, we get:
(x^2 + (2a-1)x - 2a)(x^2 + (1-a)x - a)= x^2(x^2 + (1-a)x - a) + (2a-1)x(x^2 + (1-a)x - a) - 2a(x^2 + (1-a)x - a)= x^4 + (1-a)x^3 - ax^2 + (2a-1)x^3 + (2a-1)(1-a)x^2 - (2a)^2x - 2ax^2 - 2(1-a)x + 2a^2= x^4 + (1-a+2a-1)x^3 + (-(a) - (1-a) + (2a-1)(1-a))x^2 + (-2a - 2(1-a))x + 2a^2= x^4 + ax^3 + (2a^2 - a^2 - 1 + a - 2a + 1)x^2 + (-2a + 2a)x + 2a^2= x^4 + ax^3 + (a^2 - 2)x^2 + 0 + 2a^2
Therefore, the expanded expression is:
x^4 + ax^3 + (a^2 - 2)x^2 + 2a^2 = 0
Expanding the given expression, we get:
(x^2 + (2a-1)x - 2a)(x^2 + (1-a)x - a)
= x^2(x^2 + (1-a)x - a) + (2a-1)x(x^2 + (1-a)x - a) - 2a(x^2 + (1-a)x - a)
= x^4 + (1-a)x^3 - ax^2 + (2a-1)x^3 + (2a-1)(1-a)x^2 - (2a)^2x - 2ax^2 - 2(1-a)x + 2a^2
= x^4 + (1-a+2a-1)x^3 + (-(a) - (1-a) + (2a-1)(1-a))x^2 + (-2a - 2(1-a))x + 2a^2
= x^4 + ax^3 + (2a^2 - a^2 - 1 + a - 2a + 1)x^2 + (-2a + 2a)x + 2a^2
= x^4 + ax^3 + (a^2 - 2)x^2 + 0 + 2a^2
Therefore, the expanded expression is:
x^4 + ax^3 + (a^2 - 2)x^2 + 2a^2 = 0